Solve for n.
solve for n.
−2(n − 4.5) > 11

n > 1
n < 1
n > −1
n < −1

The rate of change is found using the slope formula

m = ( y2-y1)/(x2-x1)

We have two points

( 1995, 2.54) ( 2010, 3.18)

m = (3.18-2.54) / (2010-1995)

=.64/15

$.042666666 per year

Rounding to the nearest cent

$.04 per year

We know that the price went up from 1995 to 2010 so the price increased

It increased an average of $.04 each year

A. The price of a gallon of gasoline increased by an average of $_.04__ per year from 1995 to 2010

Answer:

Step-by-step explanation:

Exact Form:

1/2

Decimal Form:

-0.5

Answer:

- 2

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

given

[tex]log_{\frac{1}{7} }[/tex] 49 = n , then

49 = [tex](\frac{1}{7}) ^{n}[/tex]

49 = [tex](7^-1)^{n}[/tex] , that is

7² = [tex]7^{-n}[/tex]

since bases on both sides are equal then equate exponents

- n = 2 ( multiply both sides by - 1 )

n = - 2

The area of the land is 289/4 square units

The area of a shape is the amount of space on the shape

For most regular quadrilaterals, you multiply the side lengths to determine the area

The given parameters are

Shape = Square

Side length = 17/2

The area of a square shape is

Area = Side length^2

So, we have

Area = (17/2)^2

Evaluate the exponent

Area = 289/4

Hence, the area of square plot of land whose each side measures 17/2 is 289/4 square units

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Answer:

20

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{50}[/tex] × [tex]\sqrt{8}[/tex]

= [tex]\sqrt{50(8)}[/tex]

= [tex]\sqrt{400}[/tex]

= 20

Answer:

(1) p(x) = 7x³ + 4x² + 6 - 9x⁴

(2) p(x) = 1 + 3x - 9x⁵

(3) y = 9x² - x³ + x⁹

(4) f(x) = (x +3)(x-2)(x+5)

Step-by-step explanation:

Standard form has terms arranged from the highest to the lowest power

Degree is the highest power

Leading coefficient is the coefficient of the highest term

Leading term is the term containing the highest power

(x + 3) (x - 2)(x + 5)

(x + 3) (x - 2) = x² + x - 6 using the FOIL method
(x² + x - 6)(x +5) = x³ + 6x² -x - 30

Step-by-step explanation:

come on, we explained this already in previous questions. if you understood the explanations there, you should have been able to some that here without any problems.

again, standard form is the sorted polynomial from highest variable exponent to the lowest (as the potential constant at the end represents the x⁰ term).

the leading term is the first term on the left (with the highest exponent).

the leading coefficient is the factor in this leading term.

degree is the highest exponent used in the polynomial (again, given by the leading term).

so, what is still the problem ?

i have a slight problem with your handwriting. it is unclear, if there is 7x³ or 17x³. or 13x or 3x.

1.

p(x) = 17x³ + 4x² + 6 - 9x⁴

now, just sort this from the highest to the lowest exponent.

p(x) = -9x⁴ + 17x³ + 4x² + 6

if it should be 7x³ instead of 17x³, please use 7x³ in the polynomial.

degree = 4

leading coefficient = -9

leading term = -9x⁴

2.

p(x) = 1 + 13x - 9x⁵

again sort from highest to lowest exponent

p(x) = -9x⁵ + 13x + 1

again, if it should be 3x instead of 13x, please use 3x in the polynomial.

degree = 5

leading coefficient = -9

leading term = -9x⁵

3.

y = 9x² - x⁵ + x⁹

remember, y = f(x)

that is the same thing, means the same thing. it just gives the result variable a specific name.

again sort by exponent.

y = f(x) or p(x) or ... = x⁹ - x⁵ + 9x²

degree = 9

leading coefficient = 1

leading term = x⁹

4.

f(x) = (x+3)(x-2)(x+5)

this is really like the other question I just answered.

so, we always multiply 2 terms. that result we multiply by the third term. and if they're are more, then that result with the fourth term, and that with the 5th term,...

I usually start at the left :

(x+3)(x-2) = x² - 2x + 3x - 6 = x² + x - 6

now

(x² + x - 6)((x+5) = x³ + 5x² + x² + 5x - 6x - 30 =

= x³ + 6x² - x - 30

so,

f(x) = x³ + 6x² - x - 30

degree = 3

leading coefficient = 1

leading term = x³

The integer values of x in the interval 3 ≤ x ≤ 9 that will satisfy the inequality include 3, 4, 5, 6, 7, 8, and 9.

It should be noted that an integer is simply used to represent a given number which can be positive.

From the information, we are given the information 3 ≤ x ≤ 9. This means that 3 is less than or equal to x and x is less than or equal to 9.

Therefore, the number that fits are from 3 to 9.

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27/4 , -3.2, -∛60 ,√48, 7.05 when arranged in ascending order we get:

-3.2 , -∛60 , 27/4 , √48, 7.05

Given list of numbers,

27/4 , -3.2 , -∛60 , √48 , 7.05.

simplifying each numbers ,

=> 27 / 4 = 6.75

=> -∛60 = - ∛(2 × 2 × 3 × 5)

= -3.9149.

=> √48  = √(2 × 2 × 2 × 2 × 2)

= 4√3

= 6.928  

So the list after simplification is ,

6.75 , -3.2 , -3.9149 , 6.928 , 7.05

Now arrange the numbers from least to greatest,

-3.2 , -3.91 , 6.75 , 6.928 , 7.05  

= -3.2 , -∛60 , 27/4 , √48, 7.05.

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Answer:8.7:1.2

Step-by-step explanation: divide both by 3

To convert a fraction to a decimal, we simply divide.

Shown below:

This is never ending decimal with the "6" repeating.

Thus, we can put a bar over "6".

So,

The cat rescue must sell 87 beds to meet the goal

The car rescue is selling cat beds as a fundraiser

The goal is to raise $1300

Each cat bed is sold at $15

The number that must be sold to reach the goal can be calculated as follows

= 1300/15

= 86.6

= ≅ 87

Hence 87 cat beds must be sold to reach the goal

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The rectangular sign is 30 feet in length and 42 feet in width.

The perimeter of the rectangular sign = 144 ft

Let the width of the rectangular sign be x, and the length of the sign will be x-12

The formula for the perimeter of the rectangle:

P = 2(l+w)

where P = perimeter of the rectangle

l = length of the rectangle

w = width of the rectangle

Substituting the values in the formula we get:

144 = 2(x-12+x)

144 = 2(2x-12)

144 = 4x -24

168=4x

x= 42

So, the length is 30ft and the width is 42ft

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Answer: (4) [tex]y=2x[/tex]

When you look at the table, you can see that the y values are double the x values they are associated with. Therefore, to get to the y value, the x values must be multiplied by 2, which would be the equation [tex]y=2x[/tex]

Based on the model that shows the altitude of Mr. Mole relative to the ground, the rate at which Mr. Mole was digging was 2.3 meters down per minute.

When given a linear function, the rate that the model progresses is given by the slope. The slope in a linear function can be found as:

y = mx + b

m =  slope

b = y-intercept

In the model given for Mr. Mole's digging, which is -2.3t - 7, the slope is -2.3.

This means that Mr. Mole is digging downwards at 2.3 meters per minute.

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Given the credit union banker's assets and liabilities, their total net worth is C. $233,693.

The net worth of an individual is the difference between their assets (long-term and short-term) and their liabilities (long-term and short-term).

The net worth is equivalent to the equity of a business, which refers to the net assets owned by the stockholders after paying off all debts.

Car Value = $29,850

Savings Accounts = $12,409

Treasury Bonds = $10,000

Checking Account Balance = $19,419

Home Value = $194,450

Total assets = $266,128

Car loan = $10,560

Student Loans = $13,824

Credit Card Balance = $8,051

Total liabilities = $32,435

Net worth = $233,693 ($266,128 - $32,435)

Thus, the banker's net worth is not $219,869, $247,517, or $252,304 but Option C.

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Answer:

$247,517

Step-by-step explanation:

ITS RIGHT ON THE TEST GUYS ! :)

When two straight lines or rays intersect at a single endpoint, an angle exists formed. If 2 and 3 exists complements, and m2= 55°, then m3 = 90 - 55 = 35 degrees.

When two straight lines or rays intersect at a single endpoint, an angle exists formed.  The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Complements sum to 90 degrees.

If 1 and 2 are complements and m1 = 35°, then

m2 = 90 - 35 = 55 degrees.

Now if 2 and 3 are complements, and m2= 55°,

then m3 = 90 - 55 = 35 degrees.

The complete question is:

Given: 1 and 2 are complements, 2 and 3 are complements, and m1 = 35°. Prove: m3 = 35° Complete the missing parts of the paragraph proof. By then, we know that angle 1 is congruent to angle 3. The measure of angle 1 equals the measure of angle 3 by the definition of angles. Then, using the property, the measure of angle 3 is the degree.

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Step-by-step explanation:

don't panic. just breathe and then use common sense.

1.

1 math question in 1/200 second

2 minutes have 2×60 seconds = 120 seconds.

each of the seconds has 200 1/200 seconds.

so, in 2 minutes we have

120 × 200 time units to finish math questions.

in each time unit 1 math question can be answered.

120×200 = 24,000

the computer can answer 24,000 math questions in 2 minutes.

2.

it can run for 15 minutes.

15 minutes have

15×60 = 900 seconds (as every minute has 60 seconds)

it can vacuum 1/2 ft² in 1 seconds.

in 900 seconds it can then vacuum 900×1/2 = 450 ft².

so, yes, it can clean 400 ft² without recharging.

Given the following functions:

to find f(g(4)), we can start by finding g(4) first:

now that we know that g(4) = 8, we can calculate the composition f(g(4)):

Answer:

f(g(4) ) = 31

Step-by-step explanation:

evaluate g(4) then substitute the value obtained into f(x)

g(4) = [tex]\frac{4^2}{2}[/tex] = [tex]\frac{16}{2}[/tex] = 8 , then

f(8) = 3(8) + 7 = 24 + 7 = 31

Answer:

2(x - 2) = 8

x = 6

Step-by-step explanation:

2(x - 2) = 8

2(x - 2) = 8

2x - 4 = 8

     +4   +4

-----------------

2x = 12

÷2   ÷2

----------

x = 6

I hope this helps!

The expression that represents the given condition is given by

5.75x + 35.

In mathematics, an expression that was created using integer variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

If x shirts are bought, cost of x shirts at $5.75 = 5.75x

Set up fee $ 35

Total cost of x shirts = 35 + 5.75x

Therefore the required expression = 35 + 5.75 x

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Answer:

2(5)+2x+2y

Step-by-step explanation:

since you both have the tickets the amount of the prize is going to double. You both also bought popcorn and soda if we take 1 popcorn as "x" it is also going to multiple 2 times same with the soda except different variable.

The maximum number of miles Julie can drive the car is 272 miles.

Let's check how:

Julie's budget for renting a car is $200.

number of days she'll rent a car is 3.

car rental per day is $44 + $0.25 per mile.

so to know maximum no. of miles she can drive

we'll first subtract the 3 days rent from Julie's budget = $200 - ( 3 x $44 )

= $200 - $132

= $132

Now, the left money is $68.

so, we will divide $68 by $0.25 to know how much miles she can drive.

= $68 ÷ $0.25

= 272 miles

Hence, the maximum number of miles Julie can drive the car for 3 days is 272 miles.

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Answer:

Step-by-step explanation:

The value of the expression 253×67 using the turtle method is given by 16951.

The turtle method of multiplication was designed in order to make the multiplication of larger numbers easier. The larger numbers can be multiplied imagining them as the form of a turtle's head and neck. It involves mainly three steps of multiplication. The first step includes the multiplication of the numbers lying on the neck of a turtle. The next step includes making the collar of the turtle, taking care of the carryovers, and laying the egg of the turtle. The last step involves the multiplication of the other numbers. In the question, we are given the expression 253×67. We multiply this expression in the turtle method as attached in the figure.

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From Option 1,2,3 and 4.

Option 3 transformation is A dilation does not always preserve distance.

Give that,

We have to find which transformation does not always preserve distance.

1 (x,y) → (x + 2, y)

2 (x,y) → (-y, -x)

3 (x,y) → (2x, y - 1)

4 (x,y) → (3-x, 2-y)

Option 3 is A dilation does not always preserve distance.

Dilation means a modification of this kind that alters the size of the image is called a dilatation. How much larger or smaller the image is is determined by the scale factor, often known as the scalar factor. A picture of each type of dilatation is shown below (one that gets larger and one that gest smaller).

Therefore, Option 3 transformation is A dilation does not always preserve distance.

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Answer:

1/24

Step-by-step explanation:

Answer:

1/24

Step-by-step explanation:

so first you cross out the 2 and 16 because 2*8=16

then you multiply the numerator and the denominator.

then bam! your answer!

1/24

The number that fills in the blank to make a perfect square trigeminal of the given expression is 81.

Given expression:

[tex]x^2+18x +[/tex] _

We have to find the number that will fill the blank.

A perfect square trigeminal is an algebraic expression that is of the form ax 2 + bx + c, which has three terms. It is obtained by the multiplication of a binomial with itself.

Let the number that fills the blank be a.

Hence, the expression becomes:-

[tex]x^2+18x +a[/tex]

To make it a perfect square geminal, the expression must be a perfect square of a binomial.

We know that,

[tex](x+y)^2=x^2+2xy+y^2[/tex]

Comparing it with given expression, we get

2xy = 18x and,

[tex]y^2=a[/tex]

Hence,

y = 9

a = [tex]9^2[/tex] = 81

Hence, the number that fills the blank is 81.

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Water used in three minutes in the shower is 12.6 gallons.

An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.

Given Data

Elyse uses 42 gallons of water for a 10-minute shower,

Let

the time in minutes at position x

y=the quantity of water in gallons

The fact that

[tex]\frac{y}{x}[/tex] = [tex]\frac{42}{10}[/tex] = 4.2x

The unit price equals

The slope of the linear equation is equal to the unit rate.

then

y=4.2x

Problem

How much water will Elyse use in her shower for three minutes?

x = 3 minutes

substituting in the previous equation

y = 4.2x

y = 4.2(3)

y = 12.6

Water used in three minutes in the shower is 12.6 gallons.

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